Limit of normalized quadrangulations: The Brownian map

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dc.creatorMarckert, Jean-François
dc.creatorMokkadem, Abdelkader
dc.date2004-03-23
dc.date2007-02-28
dc.date.accessioned2026-07-07T07:49:06Z
dc.date.available2026-07-07T07:49:06Z
dc.descriptionConsider $q_n$ a random pointed quadrangulation chosen equally likely among the pointed quadrangulations with $n$ faces. In this paper we show that, when $n$ goes to $+\infty$, $q_n$ suitably normalized converges weakly in a certain sense to a random limit object, which is continuous and compact, and that we name the Brownian map. The same result is shown for a model of rooted quadrangulations and for some models of rooted quadrangulations with random edge lengths. A metric space of rooted (resp. pointed) abstract maps that contains the model of discrete rooted (resp. pointed) quadrangulations and the model of the Brownian map is defined. The weak convergences hold in these metric spaces.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117906000000557 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0403398
dc.identifierhttp://arxiv.org/abs/math/0403398
dc.identifierAnnals of Probability 2006, Vol. 34, No. 6, 2144-2202
dc.identifierdoi:10.1214/009117906000000557
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124723
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60F99, 60K35 (Primary) 60C05, 60F05 (Secondary)
dc.titleLimit of normalized quadrangulations: The Brownian map
dc.typetext

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